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Sequence optimization for high frame rate imaging with
a convex array
Nina Ghigo, Alessandro Ramalli, Stefano Ricci, Piero Tortoli, Didier Vray,
Herve Liebgott
To cite this version:
Sequence optimization for high frame rate imaging
with a convex array
Nina Ghigo1, Alessandro Ramalli2, Stefano Ricci2, Piero Tortoli2, Didier Vray 1, Hervé Liebgott1
1Univ. Lyon, INSA-Lyon, UCBL, UJM-Saint-Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621 Lyon, France 2Department of Information Engineering, University of Florence, 50139 Florence, Italy
nina.ghigo@creatis.insa-lyon.fr
Abstract— In this paper, five different sequences for image
compounding at a high frame rate with very few sub-images are investigated for abdominal exploration with a convex probe. Simulation and experiments using a ULA-OP 256 scanner were made to compare the resolution and contrast-to-noise ratio (CNR) of the different sequences. The best configuration is based on a sliding apodization window, gives a resolution of 1° (i.e. 2.1 mm) and CNR of 12.4 dB at 6 cm depth in a Gammex Sono403™ phantom. A frame rate of 1.2 kHz can be achieved at 20 cm depth. This high-frame rate sequence has been chosen to allow the study of fast transient phenomena such as the pulse wave propagation and peak systolic velocity in deep vessels like the abdominal aorta.
Keywords—high-frame rate, compounding, virtual source, convex array
I. INTRODUCTION
Over the past two decades, new ultrasound imaging sequences referred to as high frame rate imaging have been developed. Depending on the depth of investigation, a frame rate higher than 10 kHz can be obtained using plane or diverging waves. However, if only one wave is used, this increase in frame rate comes at the price of image quality in terms of resolution and contrast. To overcome this issue, compounding techniques [1] have been developed, allowing to recover an image quality comparable to conventional focused transmissions. Several plane or diverging waves are transmitted successively in the medium with different incident angles generating backscattered echoes containing different information. By coherently combining sub-images obtained through the beamforming of the backscattered signals of each emission, a synthetic transmit focusing is achieved, which improves image quality. One drawback of compounding methods is that the final frame rate is divided by the number of sub-images to be compounded: a compromise must be reached between frame rate increase and image quality.
Optimal compounding sequences have been extensively studied for linear or phased arrays probes [2], [3]. Way less work has been carried out for convex probes. Jensen et al [4] have proposed a compounding sequence using synthetic aperture leading to a frame rate independent of the number of emissions with a convex probe. However, the rather complex computation for synthetic aperture imaging heavily affects the post-processing.
The context of this work is the development of high frame rate imaging modes for deep vessels exploration in the abdomen. In clinical practice, convex probes are used to image the abdominal cavity, as they have a larger field of view and their frequency is typically lower, allowing a deeper tissue exploration, compared to linear probes. The study of fast
phenomena in arteries, such as pulse wave propagation, high flow velocity at the systolic peak and vortex formation, has already shown its clinical value for both diagnosis, prevention, and understanding of cardiovascular diseases [5], [6]. Most of the previous work focused on the carotid artery, a shallow vessel (<3cm deep) with easy access using a linear probe, and are not directly implementable to a convex probe [7], [8]. Furthermore, the phenomena occurring in the abdominal aorta (AA) tend to be faster than those in the carotid artery. As the abdominal aorta is deeper than the carotid, the round-trip time of the ultrasound wave greatly limits the achievable frame rate. In this paper, our goal is to achieve a compounded imaging sequence allowing the study of fast phenomena while considering the limitation set by a large imaging depth.
In the following section, the clinical context of this study will be detailed. Section III presents the different compounding sequences investigated as well as the simulation and experiments carried out. The results of both simulation and experiments are presented in Section IV. Finally, Sections V and VI conclude the paper with a discussion of the results and a conclusion.
II. CLINICAL CONTEXT AND LIMITATION
The abdominal aorta (AA) is located under the abdominal fat and its depth can greatly vary from 5 to 20 cm. Its normal healthy diameter is around 2 cm. As the study of vascular diseases becomes more relevant with age and when the patient tends to be fatter, we consider the worst case condition i.e. AA being at 20 cm depth. The round-trip time of the ultrasound wave leads to a limitation of the pulse repetition frequency given by:
=
2 1)
where is the speed of sound in the medium and is the radial distance between the probe and the center of the AA. If we take equal to 1540 m/s and equals 21 cm, we obtain a maximum PRF of 3.7 kHz.
The phenomena occurring in the AA are fast and transient. The peak systolic velocity is typically around 120 cm/s while the pulse wave velocity is around 5 m/s. Typically, flow velocity is measured by Doppler techniques, over a range limitated by the Nyquist velocity:
=
4 2)
.
=4 3)
A typical convex probe has a center frequency around 3 MHz, leading to a wavelength of / ≈ 0.5 mm. If we want to observe the peak systolic velocity of the AA, we obtain a
of 1 kHz.
With these constraints on the , we can deduce that only 3 emissions can be compounded. To the best of our knowledge, no previous work has studied the compounding sequence of a convex probe with such stringent constraints.
III. MATERIALSANDMETHODS
A. Compounding sequences
In this work, five different configurations (cfg) of virtual sources (VS) spatial distributions were investigated through simulations and experiments. The CA631 convex probe (Esaote, Italy), whose parameters are given in TABLE I, was used. VS were evenly distributed on either the half-radius (haR), the radius (rad), a horizontal line through the array pivot (hoL), or the anti-radius (anR) as represented in Figure 1 a). The three VS positions were calculated with their corresponding angles (− , 0, ). Different value for , ranging from 5 to 40° in 5° steps, were tested. For cfg haR and rad, the maximum possible value is 30°, as illustrated in Figure 1. Finally, diverging waves (DWs) achieved by linear delays with a steering angle = were also tested (Figure 1 b)). The apodizations in emission and reception were given by a Hanning window over all elements of the probe, expect for the haR cfg where a sliding Hanning window of 128 elements is used in emission. These configurations are compared to a single diverging wave following the array curvature (1DW) i.e. with no delays.
B. Image formation
Each position of VS defined a different delay in emission. The backscattered echoes are beamformed with a delay-and-sum (DAS) algorithm. In this paper, we have studied the directivity of the elements to select only relevant data during the DAS summation [12].
The directivity of an element of width , depends on the insonification angle . For a piston-like element in a soft baffle (doc), which is a current assumption, it is given by [12]:
( ) = ( ) ( ( )) 4)
where is the wavelength propagating in the medium, in our case ≈ 0.5 mm. Heuristically we consider the backscattered echoes only if ( ) > 3 , leading to a directivity of approximatively 27° in our case.
In Figure 2, we represent the convex probe of center and radius . An element is displayed with its polar ( , ) and its cartesian ( , ) coordinates. Its directivity at -3dB is represented by the green cone of angle . For schematic purpose is here way bigger than typical directivity. For calculus purpose, the angle is defined between a scatterer located on z-axis and the element . The backscattered echoes from need to be considered only if they are visible by the element i.e. only if:
| − | > 5)
We can compute : =
+ − 6)
It is easily possible to go from cartesian to polar coordinates through:
Figure 2: The different configurations are represented (blue: cfg haR, red: cfg rad, green: cfg hoL, pink: cfg anR). is the angle setting the spacing between VSs and the black line represents the probe surface. b) representation of the different linear delays for cfg DWs.
TABLE I PROBE PARAMETERS Number of elements 192
Radius of curvature = 60.3 mm
Field of view -30°/30°
TABLE II ACQUISITION PARAMETERS Transmit frequency = 3.5 MHz
Sampling frequency 12.5 MHz in simulation 39 MHz in experiments Transmit burst 3-cycle sinusoidal burst Speed of sound = 1540 m/s
Pulse repetition frequency = 3000 Hz Transmit apodization
Hanning on all elements Sliding Hanning on 128 elements for cfg haR
Receive apodization Hanning on all elements Number of scatterers per mm²
for simulation ≈ 2000
D
epth (
cm
)
Figure 1: Representation of the notion of directivity with a convex probe of center and radius . is an element of the probe and a scatterer.
= ( )
= ( ) 7)
Equation 6) then becomes:
= ( )
+ 1 − ( ) 8)
As | − | is known for each element of the probe, it is possible to determine for every point of interest in the medium if it should be considered or not.
C. Data acquisition
Simulations were performed through SIMUS [13] on two 6 cm deep anechoic cysts aligned ° and angled at 15° ° with
the probe (Figure 3).
Experiments were performed using a ULA-OP 256 scanner [14] and a CA631 Esaote convex probe on the Gammex Sono403™ phantom. We focus our attention on the scatterer and the anechoic cyst located at 6 cm (Figure 4).
Simulation and experiment parameters are shown in Table II. D. Performance measures
The resolution, measured as the width of the PSF at -6 dB, is computed on the data in polar coordinates, which leads to a resolution in radian or degree. This is done to evaluate the resolution in the correct direction of the PSF. The following equation is used to convert the resolution in radian to
meter knowing the radial distance where the resolution was computed:
= ( + ) 9)
Similarly, the contrast to noise ratio (CNR) is computed on the final compounded image B-mode in polar coordinates to avoid the influence of interpolation.
= 20 ( −
+ 2
) 10)
where and ( and ) are the means (variances) pixel values, after log compression, of the cyst and the background regions, respectively.
IV. RESULTS
The CNR values obtained on the compounded final image in simulation and experimentation are reported in Figure 5.
A. Simulation
In simulation, the CNR obtained on the centered and angled cysts vary quite irregularly with the cfg and angle. The maximum difference in terms of contrast is less than 1 dB, which is quite low. With only the simulated data it is impossible to conclude on the best cfg. The CNR obtained on the centered and angle cysts with only one diverging wave (1DW) is 12.6 and 10.8 dB, respectively.
B. Gammex experimentation
In terms of resolution, cfg DWs gives poor results, showing the great difference between the use of a linear and convex probe. cfg rad, hoL and anR give pretty similar results, which is coherent as their VS are near to each other. The best angle for theses cfg is 15°, where the resolution is less than 1.1° i.e. 2.3 mm thanks to 9). The cfg giving the best resolution is haR where its minimum resolution of 0.95° (2 mm) is obtained at
= 25°.
The cfg behave similarly for the CNR, where cfg DWs gives the poorest results, cfg rad, hoL and anR have similar behavior with a best CNR higher than 12 dB at = 5°. For cfg haR, the best CNR of 12.4 dB for = 20°.
For the cfg haR (the best one), if we both consider resolution and CNR, the best angles are = 25° and = 20° respectively. For = 25°, the CNR decreased rather heavily at 11.15 dB. For = 20°, the resolution increased by less than 0.05° leading to a resolution of 1° (2.1 mm).
The best compromise between resolution and CNR seems then to be the sliding cfg haR at = 20° displayed in Figure 4. For comparison purposes, the worst-case image (cfg DWs; =5°) alongside with 1DW (no compounding) are also displayed. The CNR and resolution obtained with only one diverging wave (1DW) is respectively 9.1 dB and 1°.
V. DISCUSSION
The best configuration in terms of image quality in both resolution and contrast-to-noise ratio has been investigated. Other performance measures could have been used, such as speckle size measurement [4].
Figure 3:
The scatterers (a) and the anechoic cysts (b) positions used in simulation are sketched.
The reason for the discrepancy we observe on the CNR obtained in simulation versus the experiments remains unknown and will be the subject of further investigations. For a linear array, one of the most used sequences is angled linear delays, done in cfg DWs. For a convex probe, cfg DWs gives the poorest results highlighting the need of specific compounding sequences for convex probes. As shown in III.B, only relevant data should be considered during image formation. This may explain why the best configuration is the one with a sliding window apodization that does not consider all elements (cfg haR). Similarly, sending one diverging wave in the medium (cfg 1DW) can give a better image quality than a poor compounding sequence.
VI. CONCLUSION
In this paper, a configuration of three virtual sources was presented for high-frame rate compounding. The goal of future work will be to use this sequence in an abdominal aorta phantom to estimate simultaneously the motion of the blood flow and the wall.
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Figure 5: The CNR obtained on the simulated anechoic cysts are showed in a) and b). The resolution in degree, and CNR, obtained on the 6 cm-deep scatterer of the Gammex phantom are showed in b) and c).
12.7 12.9 13.1 13.3 13.5 5° 10° 15° 20° 25° 30° 35° 40° CN R ( d B) βangle
